.... the facts about the whereabouts of Bix in January1929, a witness testimony (second hand, I admit) and what your ears tell you when you hear the various takes of Miller's "Cradle of Love." However, your hypothesis of a over-recording by Bix on three takes of Miller's "Cradle of Love" is far-fetched. Here are the two principal objections.
1. Although not technically impossible, we are talikng about a rather elaborate project. First, the band had to record the three takes and play all the accompaniments to the solos as if the solos were being played. Then, the record had to be played and Bix (or the mystery soloist) had to play the solos at the appropriate times and the whole thing (sound from the initial record and sound from the solo) recorded again. It was not technically possible at the time to take a recording with a solo played by another trumpet player, remove the solo part and record over the solo by Bix/mystery cornetist. Even if the procedure I suggested was used, it would very easy to tell by ear that one part of the recording was pre-recorded and that the solos were recorded over the pre-recorded record. Mixing as we know today was not available at the time. Would the Ray Miller band play "Cradle of Love" assuming that a solo would be added later? I seriously doubt it.
2. Why would Brunswick go through such an elaborate procedure? It is not as if a solo by Bix (anonymous) would result in fantastic sales of the records. There is no reason why a solo by Bix (and uncredited at that) would warrant the Miller band and Brusnwick going through the elaborate procedure described above.
For me the analysis is straightforward. Bix's whereabouts in Jan 1929, a witness account, and what I hear all lead me to the fairly certain (99% plus) conclusion that the mystery cornetist is not Bix. I don' know who it is. There were tens of competent musicians -highly influenced by Bix- capable to do the three takes -not that radically different from each other in my opinion *see note*, and not that fantastic/unusual an improvisation- in succession.
Note. The German (non-vocal) take seems different, at least in part, because of the strong string bass beat in it, something not so prominently used in the previous two takes.